Maximal complexifications of certain homogeneous Riemannian manifolds
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- by S. Halverscheid and A. Iannuzzi PDF
- Trans. Amer. Math. Soc. 355 (2003), 4581-4594 Request permission
Abstract:
Let $M=G/K$ be a homogeneous Riemannian manifold with $\dim _{\mathbb {C}} G^{\mathbb {C}} = \dim _{\mathbb {R}} G$, where $G^{\mathbb {C}}$ denotes the universal complexification of $G$. Under certain extensibility assumptions on the geodesic flow of $M$, we give a characterization of the maximal domain of definition in $TM$ for the adapted complex structure and show that it is unique. For instance, this can be done for generalized Heisenberg groups and naturally reductive homogeneous Riemannian spaces. As an application it is shown that the case of generalized Heisenberg groups yields examples of maximal domains of definition for the adapted complex structure which are neither holomorphically separable nor holomorphically convex.References
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Additional Information
- S. Halverscheid
- Affiliation: Carl von Ossietzky Universität, Fachbereich Mathematik, D-26111 Oldenburg i. O., Germany
- Email: halverscheid@mathematik.uni-oldenburg.de
- A. Iannuzzi
- Affiliation: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, I-40126 Bologna, Italy
- Email: iannuzzi@dm.unibo.it
- Received by editor(s): December 31, 2001
- Received by editor(s) in revised form: November 18, 2002
- Published electronically: July 8, 2003
- Additional Notes: The first author was partially supported by SFB 237, “Unordnung und große Fluktuationen"
The second author was partially supported by University of Bologna, funds for selected research topics - © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 4581-4594
- MSC (2000): Primary 32C09, 53C30, 32M05; Secondary 32Q28
- DOI: https://doi.org/10.1090/S0002-9947-03-03263-X
- MathSciNet review: 1990763